In recent years, an optical element which forms a stereoscopic real image using a micromirror array element in which a large number of a pair of orthogonal micromirror elements are arranged has been developed.
Since early times, the eye of a lobster and the like has long been known as a lobster optical system corresponding to an imaging device in which a large number of quadrangular-prism-shaped reflective optical elements with mirror side surfaces are arranged on a spherical surface. The lobster optical system uses reflection, and thus has mainly been studied and developed in the area of a band of the wavelength for X rays, infrared rays or the like, which is difficult or expensive to obtain the material having a desired refractive index therefor.
It has been pointed out that a large number of the reflective optical elements described above are arranged on a flat plane instead of a spherical surface to form a stereoscopic real image. This will be described with reference to FIGS. 1A and 1B. FIGS. 1A and 1B are schematic views illustrating the structure of the conventional reflective optical element. FIG. 1A is a perspective view of a reflective optical element, whereas FIG. 1B is a plan view of the reflective optical element. In the description below, the spatial coordinate axes are referred to as XYZ axes. The X-axis, Y-axis and Z-axis are orthogonal to one another. As illustrated in FIGS. 1A and 1B, a large number of (three in FIGS. 1A and 1B) reflective optical elements 1 each having the shape of a quadrangular prism are arranged on an XY plane. The bottom surface of each reflective optical element 1 has the shape of a square, and each reflective optical element 1 is disposed on the XY plane such that the sides of the bottom surface thereof are aligned with the X-axis and Y-axis directions, respectively. Meanwhile, the height direction (axial direction) of each reflective optical element 1 is aligned with the Z-axis direction. An upper surface A′ and a lower surface (bottom surface) A of each reflective optical element 1 are transparent, so that light can enter therethrough and be output therefrom. On the other hand, side surfaces B, B′, C and C′ of each reflective optical element 1 are so formed that at least two adjacent ones of the side surfaces are mirror surfaces which can reflect light.
Next, for the reflective optical element 1 illustrated in FIGS. 1A and 1B, transmission of an incident light ray inside the reflective optical element 1 in the case where the light ray enters through the bottom surface will be described with reference to FIGS. 2A and 2B. FIGS. 2A and 2B are schematic views illustrating reflection of light ray in the conventional reflective optical element 1. FIG. 2A illustrates the state of a light ray when the reflective optical element 1 is seen from the X-axis direction, whereas FIG. 2B illustrates the state of a light ray when the reflective optical element 1 is seen from the Z-axis direction. In the examples illustrated in FIGS. 2A and 2B, the incident light ray enters from a point a on the lower surface A, and thereafter travels straight to reach a point b on the side surface C′ at which it is reflected. The light ray reflected at the side surface C′ is further reflected again at a point c on the side surface B, and is output from a point d on the upper surface A′. As can be seen from FIG. 2A, the light ray entering the reflective optical element 1 at an incident angle θ1 is output at an output angle θ1. Furthermore, as illustrated in FIG. 2B, the projection of the incident light ray onto the lower surface A (XY plane) has the same size as the projection of the output light ray onto the upper surface A′ (XY plane). That is, in FIG. 2B, the projection of the incident light ray onto the lower surface A is in an antiparallel state with the projection of the output light ray onto the upper surface A′.
In view of the description above, the mechanism of image forming in the case where a large number of reflective optical elements 1 are arranged will be described with reference to FIGS. 3A and 3B. FIGS. 3A and 3B are schematic views illustrating double reflection and image forming in the conventional reflective optical element 1. FIG. 3A illustrates the reflective optical elements 1 and 2 when seen from the X-axis direction, whereas FIG. 3B illustrates the reflective optical elements 1 and 2 when seen from the Z-axis direction. In the example illustrated in FIGS. 3A and 3B, the light ray from a point light source 20 enters the lower surface A of each of the reflective optical elements 1 and 2. The light ray from the point light source 20 enters the lower surface A of the reflective optical element 1 at the incident angle θ1. As has already been described, the incident light ray is output from the upper surface A′ of the reflective optical element 1 at the output angle θ1. Here, as illustrated in FIG. 3B, the output light ray at the upper surface A′ (XY plane) travels inversely to the direction of the incident light ray at the lower surface A (XY plane). Moreover, the light ray from the point light source 20 enters the lower surface A of the reflective optical element 2 at an incident angle θ2, and the light ray is output from the upper surface A′ of the reflective optical element 2 also at the output angle θ2. Accordingly, the output light rays from the two reflective optical elements 1 and 2 intersect with each other again.
As described above, it can be seen that the light rays from the point light source 20 are condensed again after passing through the reflective optical elements 1 and 2 to form a double reflection image 21. As illustrated in FIG. 3A, assuming that the distance between the point light source 20 and the arrangement surfaces (lower surfaces A) of the reflective optical elements 1 and 2 is L, it can be seen that the distance L is equal to a distance L′ between the image (here, the double reflection image 21) and the arrangement surfaces (upper surfaces A′) of the reflective optical elements 1 and 2, and that the position of the image is symmetrical to the point light source 20 with respect to the arrangement surfaces of the reflective optical elements 1 and 2 (specifically, the surface passing through the middle between the lower surfaces A and the upper surfaces A′).
As described above, the image is formed by the light rays (twice-reflected light rays) that are reflected twice in the respective reflective optical elements 1 and 2. However, it has also been known that a single reflection image is formed by the light rays (once-reflected light rays) that are reflected once in the reflective optical elements 1 and 2. This will be described with reference to FIGS. 4A and 4B. FIGS. 4A and 4B are schematic views illustrating single reflection and image forming in the conventional reflective optical elements 1 and 2. FIG. 4A illustrates the reflective optical elements 1 and 2 when seen from the X-axis direction, whereas FIG. 4B illustrates the reflective optical elements 1 and 2 when seen from the Z-axis direction. In the example illustrated in FIGS. 4A and 4B, the light rays from the point light source 20 enter the lower surfaces A of the reflective optical elements 1 and 2, respectively, are reflected once at points P and Q on the respective side surfaces C of the reflective optical elements 1 and 2, are thereafter output from the upper surfaces A′ of the reflective optical elements 1 and 2, and are condensed again to form an image (single reflection image 22). As can be seen from the description above, the single reflection image 22 is more prominent when observed from the direction parallel to the sides on the lower surfaces A of the reflective light source elements 1 and 2 (Y-axis direction in FIGS. 4A and 4B).
On the other hand, the double reflection image 21 is more intense in the diagonal line direction of the lower surfaces A of the reflective optical elements 1 and 2, as can be understood from the illustration of FIGS. 2A to 3B. Accordingly, the double reflection image 21 and the single reflection image 22 have different observing directions on the XY plane, which allow only the double reflection image 21 to be seen by setting the observing orientation to the diagonal line direction of the bottom surfaces A of the reflective optical elements 1 and 2.
The resolution of the double reflection image 21 is determined by the size of the reflective optical elements 1 and 2. It is therefore desirable in practice to employ the reflective optical elements 1 and 2 each having one side of the bottom surface A being 0.5 mm or shorter. In addition, it is understood that the image is brighter if the thickness (height in the Z-axis direction) of the reflective optical elements 1 and 2 is larger. Thus, for the reflective optical elements 1 and 2, a shape with a high aspect ratio, i.e. a small bottom surface A and a large thickness (height), is desired. On the other hand, in order to obtain a large stereoscopic image, it is necessary to produce an array of reflective optical elements having a large area (size) in which a large number of reflective optical elements 1 and 2 are arranged.
It is however difficult in terms of a production method to prepare at a time the array of reflective optical elements with a large area including a large number of reflective optical elements 1 and 2 each having a high aspect ratio and a microscopic shape. Thus, such a method has been considered as to prepare a plurality of small pieces each having a relatively small area and connect the small pieces with one another on a plane to form an array of reflective optical elements having a large area (see International Publication No. WO2013/061619, for example). This is called tiling, and each of the small pieces is called a tile.
FIGS. 5A to 6 are schematic views illustrating the tiling structures of the conventional reflective optical elements. FIG. 5A illustrates the tiles when seen from the X-axis direction, whereas FIGS. 5B and 6 illustrate the tiles when seen from the Z-axis direction. International Publication No. WO2013/061619 has proposed to prepare square tiles 3 each having multiple reflective optical elements 1 arranged on the XY plane and arrange the multiple tiles 3 on the XY plane, as illustrated in FIGS. 5A and 5B, to obtain an array of reflective optical elements having a larger area. International Publication No. WO2013/061619 has also proposed, as illustrated in FIG. 6, to prepare fan-shaped tiles 4 in which multiple reflective optical elements 1 are arranged in a fan-like shape, and combine the multiple fan-shaped tiles 4 together to obtain a substantially circular array of reflective optical elements. Here, the ends of the tiles 3 and 4 have broken side surfaces that are reflective plates, which generate reflected light causing undesirable noise if they remain broken, and the light is irregularly reflected in directions different from the intended reflecting direction. To prevent this, International Publication No. WO2013/061619 describes that a light shielding part 5 is provided by applying a light shielding process to the ends of the tiles 3 and 4 to suppress unnecessary reflection.